Question

Tanisha goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Tanisha decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Tanisha paid.

Answer 1

To calculate the total amount that Tanisha paid, we need to consider the subtotal, the tax, and the tip.

1. **Subtotal**: The subtotal is \( xx \) dollars.

2. **Tax**: The tax is 5% of the subtotal. Therefore, the amount of tax is:
\[
\text{Tax} = 0.05 \times xx
\]

3. **Total after tax**: The total amount after adding the tax to the subtotal is:
\[
\text{Total after tax} = xx + 0.05 \times xx = xx(1 + 0.05) = xx \times 1.05
\]

4. **Tip**: Tanisha leaves a tip of 15% on the total amount including the tax. Thus, the tip is:
\[
\text{Tip} = 0.15 \times (xx \times 1.05)
\]

5. **Total amount paid**: The total amount that Tanisha paid is the total after tax plus the tip:
\[
\text{Total amount paid} = \text{Total after tax} + \text{Tip}
\]
Substituting in the values calculated, we have:
\[
\text{Total amount paid} = (xx \times 1.05) + (0.15 \times (xx \times 1.05))
\]

Factoring out \( xx \times 1.05 \):
\[
\text{Total amount paid} = xx \times 1.05 \times (1 + 0.15) = xx \times 1.05 \times 1.15
\]

6. **Final expression**: Therefore, the total amount that Tanisha paid can be expressed as:
\[
\text{Total amount paid} = xx \times 1.05 \times 1.15
\]
Simplifying this further gives:
\[
\text{Total amount paid} = xx \times 1.2075
\]

In conclusion, the expression for the total amount Tanisha paid is:
\[
xx \times 1.2075
\]